Bundle gerbes

Michael K. Murray

RECORD

Bundle gerbes

Michael K. Murray

dg-ga · Submitted 25 Jul 1994

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Every bundle gerbe gives rise to a gerbe and most of the well-known examples examples of gerbes are bundle gerbes.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,609 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.12 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.80 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

Just as $\Cstar$ principal bundles provide a geometric realisation of two-dimensional integral cohomology; gerbes or sheaves of groupoids, provide a geometric realisation of three dimensional integral cohomology through their Dixmier-Douady class. I consider an alternative, related, geometric realisation of three dimensional cohomology called a bundle gerbe. Every bundle gerbe gives rise to a gerbe and most of the well-known examples examples of gerbes are bundle gerbes. I discuss the properties of bundle gerbes, in particular bundle gerbe connections and curvature and their associated Dixmier-Douady class.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Just as $\Cstar$ principal bundles provide a geometric realisation of two-dimensional integral cohomology; gerbes or sheaves of groupoids, provide a geometric realisation of three dimensional integral cohomology through their Dixmier-Douady class.	background 1.00	0.06	0.10	asserted 1.00
s1	I consider an alternative, related, geometric realisation of three dimensional cohomology called a bundle gerbe.	contribution 1.00	0.83	0.24	asserted 0.98
s2	Every bundle gerbe gives rise to a gerbe and most of the well-known examples examples of gerbes are bundle gerbes.	result 0.75	0.32	0.19	asserted 1.00
s3	I discuss the properties of bundle gerbes, in particular bundle gerbe connections and curvature and their associated Dixmier-Douady class.	contribution 0.99	0.77	0.13	asserted 0.85

What kind of paper the classifier reports this is: method or tool 0.59 · evidence from proof or derivation 0.72.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

Just as $\Cstar$ principal bundles provide a geometric realisation of two-dimensional integral cohomology; gerbes or sheaves of groupoids, provide a geometric realisation of three dimensional integral cohomology through their Dixmier-Douady class. I consider an alternative, related, geometric realisation of three dimensional cohomology called a bundle gerbe. Every bundle gerbe gives rise to a gerbe and most of the well-known examples examples of gerbes are bundle gerbes. I discuss the properties of bundle gerbes, in particular bundle gerbe connections and curvature and their associated Dixmier-Douady class.

Human review

How Pith checks papers → · Full audit of this paper →

References

Forward citations

Cited by 7 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Weak Lie 3-groups, 2-gerbes over torus fibrations of type F1, and T-Duality
math.DG 2026-09 conditional novelty 6.0 of 10

Explicit weak Lie 3-groups for the 2-category of gerbes over a torus are constructed, a homotopy equivalence between two models is proven, and dimensional reduction reproduces the Nikolaus-Waldorf T-duality 2-groups.
On Quantum Aspects of 1-Form Symmetries I: BV-BRST Cohomology and Anomaly Polynomials
hep-th 2026-06 unverdicted novelty 6.0 of 10

Develops Čech-de Rham bicomplex from gerbe data for BV-BRST cohomology of U(1) 2-form gauge theories and anomaly polynomials of 1-form symmetries.
The character map in (twisted differential) non-abelian cohomology
math.AT 2020-09 conditional novelty 6.0 of 10

A unified non-abelian character map is constructed that recovers the Chern-Dold, Chern-Weil, and Cheeger-Simons characters and extends them to higher twisted cohomology.
Extended Riemannian Geometry I: Local Double Field Theory
hep-th 2016-11 accept novelty 6.0 of 10

A graded-manifold framework called extended Riemannian geometry reproduces double field theory's symmetries and yields a coordinate-invariant form of its strong section condition.
M2-branes, Higher Form Symmetries and 1-Gerbes
hep-th 2026-02 conditional novelty 5.0 of 10

A torsion gerbe on the M2-brane worldvolume cancels a mixed higher-form anomaly, breaking U(1) symmetries to discrete subgroups and imposing a worldvolume flux condition.

Show 2 more citing papers

Multiple M5-branes, String 2-connections, and 7d nonabelian Chern-Simons theory
hep-th 2012-01 conditional novelty 5.0 of 10

The holographic dual of multiple M5-branes is proposed to be a 7d nonabelian Chern-Simons theory of twisted String 2-connections, defined globally on a smooth moduli 2-stack.
An Invitation to Higher Gauge Theory
hep-th 2010-03 conditional novelty 3.0 of 10

Higher gauge theory describes string parallel transport as a 2-functor from a path 2-groupoid to a Lie 2-group, with the 1-form and 2-form tied by t(B) = dA + A wedge A, and six families of Lie 2-groups cover the know...

How later papers used it

61 later papers cite it

Evidence: substantial. 60 of the citing papers share no author with it, and 10 of those carry a confident label from Pith's citation classifier.

Pith read 28 of the 138 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

5 later papers by other authors are listed below: 2 built on it and 3 used its method or tool.

Builds on it 2 of 5 papers with this label

Extended this paper's existence result, since its assumption is satisfied for an abelian 2-group.

A global perspective to connections on principal 2-bundles (2016) · 1.00 · paraphrased: the licence does not allow quoting
Introduced diffeological A-bundle gerbes very similar to the bundle gerbes introduced by this paper, allowing the replacement of the structure and internal diffeological spaces.

Transgression to Loop Spaces and its Inverse, II: Gerbes and Fusion Bundles with Connection (2010) · 0.89 · paraphrased: the licence does not allow quoting

Uses its method or tool 3 of 5 papers with this label

Used the theory of ordinary lifting bundle gerbes from this paper to re-assemble data into a principal LΓ-bundle over LM.

Lifting Problems and Transgression for Non-Abelian Gerbes (2011) · 0.99 · paraphrased: the licence does not allow quoting
Followed this paper to lift the Čech cocycle to an isomorphism of potentially non-trivial bundles over Y^[2].

The 2-Hilbert Space of a Prequantum Bundle Gerbe (2016) · 0.93 · paraphrased: the licence does not allow quoting
For this we follow [ref] .

Discrete torsion in gauging non-invertible symmetries (2024) · Non-invertible gauge actions on B-fields · 0.83

How the literature uses it

61 arXiv papers cite this in 138 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 75 sentences without a confident label

Builds on it 5 papers

This assumption is, for instance, satisfied in the case of an abelian 2-group, so that our result is an extension of Murray's existence result [ref] .

A global perspective to connections on principal 2-bundles · Introduction · 1.00
Let us now generalise this observation to $(1)$-bundle gerbes following [ref] .

The 2-Hilbert Space of a Prequantum Bundle Gerbe · Connective structures · 0.95
One ingredient we use is a generalization of a lemma of Murray [ref] about differential forms on fibre products of a surjective submersion from the smooth to the diffeological setting – this is discussed in Appendix [ref].

Transgression to Loop Spaces and its Inverse, III: Gerbes and Thin Fusion Bundles · Main Theorems · 0.98

Uses its method or tool 5 papers

Third, we re-assemble these into a principal $LΓ$-bundle over $LM$ using the theory of (ordinary) lifting bundle gerbes [ref] .

Lifting Problems and Transgression for Non-Abelian Gerbes · Introduction · 0.99
This reformulation is based on work of Murray [ref] , Gomi [ref] , and previous work [ref] .

String geometry vs. spin geometry on loop spaces · Method of proof and organization of the paper · 0.87
We now follow [ref] and lift the Čech cocycle $Φ_2$ to an isomorphism of potentially non-trivial $(1)$-bundles over $Y^[2]$.

The 2-Hilbert Space of a Prequantum Bundle Gerbe · Definitions · 0.93

Compares with it 2 papers

We can thus compare it with the holonomy of the abelian bundle gerbe $𝒢$, which has been defined in [ref] , see also [ref] .

Connections on non-abelian Gerbes and their Holonomy · Holonomy around Surfaces · 0.99
Compared to the classical definition of a bundle gerbe [ref] , we have made two independent generalizations.

Transgression to Loop Spaces and its Inverse, II: Gerbes and Fusion Bundles with Connection · Bundle Gerbes · 0.89

Cites it as support 1 paper

In fact, the de Rham cohomology class of $ω$ coincides with the image of the Dixmier-Douady class under the inclusion $H^3(X,)→H^3(X,)$ [ref] .

Geometric and topological aspects of Type IIB D-branes · Bundle gerbe connections · 0.98

Cites it as background 40 papers

Bundle gerbes were originally introduced in [ref] and the definition of their gauge transformation was defined later in [ref] .

The puzzle of global Double Field Theory: open problems and the case for a Higher Kaluza-Klein perspective · Introduction · 0.98
If the fibre $ΛX_x ≃G$ for every $x∈X_0$ then this gives a $G$-gerbe in the sense of [ref] , that is, an extension of groupoids [equation] However, we wish to use a mental picture as close to bundle gerbes [ref] as possible, so offer the following diagram encoding a gerbe $X→M$: [equation] We have left and right actions of $ΛX$ on $X_1$, or rather a left action of $ΛX_L :=_1^* ΛX$ and a right action of $ΛX_R :=_2^* ΛX$ on $X_1$, preserving the fibres of $(s,t)$, by composition in the groupoid $X$.

Smooth loop stacks of differentiable stacks and gerbes · Recap on differentiable gerbes · 0.95
The Kalb-Ramond field is, geometrically, the connection of a bundle gerbe $𝒢↠M$, a categorification of a $U(1)$-bundle, which was introduced by [ref] and reformulated in terms of Čech cohomology by [ref] .

Towards an extended/higher correspondence -- Generalised geometry, bundle gerbes and global Double Field Theory · Introduction · 0.87

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.